Discrete mathematics underpins all of computer science. These books cover the essential topics: logic, proof techniques, set theory, combinatorics, graph theory, and number theory.
Foundational Discrete Math Textbooks
Standard undergraduate discrete mathematics textbooks.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| Discrete Mathematics and Its Applications 8th Edition, McGraw-Hill | Kenneth H. Rosen | 2019 | Beginner-Intermediate | The most widely adopted discrete math textbook. Clear coverage of logic, proofs, sets, combinatorics, graphs, and number theory. |
| Discrete Mathematics with Applications 5th Edition, Cengage | Susanna S. Epp | 2019 | Beginner-Intermediate | Exceptional at teaching mathematical reasoning and proofs. The best text for students new to formal mathematics. |
| Discrete Mathematics: An Open Introduction 3rd Edition, Open Textbook | Oscar Levin | 2019 | Beginner | Free open textbook covering the standard discrete math curriculum. |
Combinatorics
Enumeration, permutations, combinations, and combinatorial structures.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| A Walk Through Combinatorics 4th Edition, World Scientific | Miklós Bóna | 2016 | Intermediate-Advanced | Engaging introduction to combinatorics with excellent balance of depth and accessibility. |
| Enumerative Combinatorics, Volumes 1 & 2 Cambridge University Press | Richard P. Stanley | 2012, 1999 | Advanced | The definitive advanced reference on enumerative combinatorics. |
| Combinatorics: Topics, Techniques, Algorithms Cambridge University Press | Peter J. Cameron | 1994 | Advanced | Broad survey of combinatorial topics with an algorithmic flavor. |
Graph Theory
Theory and applications of graphs.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| Introduction to Graph Theory 2nd Edition, Pearson | Douglas B. West | 2001 | Intermediate-Advanced | The standard graph theory textbook with rigorous proofs and comprehensive coverage. |
| Graph Theory 5th Edition, Springer | Reinhard Diestel | 2017 | Advanced | Graduate-level graph theory text covering classical and modern results. Available freely online via the author's website. |
| Graphs and Digraphs 6th Edition, CRC Press | Gary Chartrand, Linda Lesniak, Ping Zhang | 2015 | Intermediate | Accessible graph theory textbook with extensive examples and exercises. |
Logic and Proof
Mathematical logic, proof techniques, and theorem proving.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| How to Prove It 3rd Edition, Cambridge University Press | Daniel J. Velleman | 2019 | Beginner-Intermediate | The best introduction to writing mathematical proofs. Essential for CS students transitioning to theoretical courses. |
| Mathematical Logic 2nd Edition, Springer | H.-D. Ebbinghaus, J. Flum, W. Thomas | 1994 | Advanced | Rigorous introduction to mathematical logic including completeness and Gödel's theorems. |
| A Mathematical Introduction to Logic 2nd Edition, Academic Press | Herbert B. Enderton | 2001 | Advanced | Standard logic textbook used in mathematics departments. |
Number Theory and Applications
Classical and modern number theory with CS applications.
| Book | Author | Year | Level | Description |
|---|---|---|---|---|
| Concrete Mathematics 2nd Edition, Addison-Wesley | Ronald L. Graham, Donald E. Knuth, Oren Patashnik | 1994 | Advanced | Knuth's unique blend of continuous and discrete mathematics. Essential for algorithm analysis. |
| An Introduction to the Theory of Numbers 6th Edition, Oxford | G.H. Hardy, E.M. Wright | 2008 | Advanced | Classic number theory textbook by two of the 20th century's great mathematicians. |
| A Course in Number Theory and Cryptography 2nd Edition, Springer | Neal Koblitz | 1994 | Advanced | Number theory motivated by cryptographic applications, suitable for CS students. |